When I set my '65 Varsity up with long-reaching(!) Weinmann sidepull calipers and with the very basic old model Matthauser blocks with crimped alloy holders, the thicker pads resulted in too much squish at the lever despite the pad's surfaces being perfectly mated at the rim sidewall.
This was with mis-matched Record/Veloce 10s Ergolevers.
As a last-ditch fix that might allow me to retain the stock calipers, I changed to longer, newer-style Kool-Stop dual-compound MTB pads, and lo and behold I got a solid feel at the lever with plenty of braking power at least for my 150# self on more-spirited (i.e. training) rides.
Moral of this story is that if one perseveres with those flimsy old calipers that some good braking power can be found, with a good balance of leverage/travel and actual stopping performance.
Note also that today's thinner pads are for the most part backed up by thicker mounting hardware, including a plain spacer
plus one matched set orbital swivel washer. So not too much if any total thickness is lost in most cases.
Using pads of different thickness does not change the pad-dive (or pad-rise) trajectory of the pad surface at the rim at all. But as I think Salamandrine mentioned, the thicker pad will have greater thickness variation over it's life and so will over time result in greater pad contact position change on the rim sidewall (toward the tire).
Plenty of leverage and brake power as shown (using Kool-Stop BMX pads):
